ABSTRACT
This chapter briefly explains three methods of minimization such as algebraic minimization, Karnaugh map, and Quine-McCluskey algorithm. It presents several examples of each method. Algebraic minimization uses the axioms and theorems of Boolean algebra developed by George Boole in 1854 and later put into practice by Claude E. Shannon who showed how to adapt the algebra to describe logic circuits. A Karnaugh map presents a clear indication of function minimization without recourse to Boolean algebra and will generate a minimized expression in either a sum-of-products form or a product-of-sums form. The Karnaugh map is arranged as an array of squares in which each square represents a binary value of the input variables. The Quine-McCluskey algorithm is used to minimize a logic function with a large number of variables and is easily converted to a computer program. The rationale for the Quine-McCluskey method relies on the repeated application of the distributive and complementation laws.
